What he used is called a cabinet scraper. It’s a thin piece of tempered tool steel with a burr raised on the edge. You scrape the burr along the surface to peel off a very thin layer. It’s the old-fashioned cabinet-makers’ way of smoothing wood. They take a little practice to learn how to use and sharpen but good quality ones are very nice tools to have in the woodshop and apparently in the finishing department of the printshop as well.

If you absolutely do not have access to one, you could try sanding in a single direction.
The direction would be moving down the bevel as it were, and some #220 sandpaper would do the job; but you will not end up with a polished edge like a good sharp cutting tool will give.